Bargaining with commitments

We study a simple bargaining mechanism in which each player puts a prize to his resources before leaving the game. The only expected final equilibrium payoff can be defined by means of selective marginal contributions vectors, and it coincides with the Shapley value for convex games. Moreover, for 3-player games the selective marginal contributions vectors determine the core when it is nonempty.demand commitment game bargaining

The Harsanyi paradox and the 'right to talk' in bargaining among coalitions

We introduce a non-cooperative model of bargaining when players are divided into coalitions. The model is a modification of the mechanism in Vidal-Puga (Economic Theory, 2005) so that all the players have the same chances to make proposals. This means that players maintain their own 'right to talk' when joining a coalition. We apply this model to an intriguing example presented by Krasa, Tamimi and Yannelis (Journal of Mathematical Economics, 2003) and show that the Harsanyi paradox (forming a coalition may be disadvantageous) disappears.cooperative games bargaining coalition structure Harsanyi paradox

A bargaining approach to the consistent value for NTU games with coalition structure

The mechanism by Hart and Mas-Colell (1996) for NTU games is generalized so that a coalition structure among players is taken into account. The new mechanism yields the Owen value for TU games with coalition structure as well as the consistent value (Maschler and Owen 1989, 1992) for NTU games with trivial coalition structure. Furthermore, we obtain a solution for pure bargaining problems with coalition structure which generalizes the Nash (1950) bargaining solution.NTU consistent bargaining stationary subgame perfect equilibrium

Negotiating the membership

In cooperative games in which the players are partitioned into groups, we study the incentives of the members of a group to leave it and become singletons. In this context, we model a non-cooperative mechanism in which each player has to decide whether to stay in his group or to exit and act as a singleton. We show that players, acting myopically, always reach a Nash equilibrium.Cooperative game, coalition structure, Owen value, Nash equilibrium

Implementation of the levels structure value

We implement the levels structure value (Winter, 1989) for cooperative transfer utility games with a levels structure. The mechanism is a generalization of the bidding mechanism by Perez-Castrillo and Wettstein (2001).levels structure value implementation TU games

Forming societies and the Shapley NTU value

We design a simple protocol of coalition formation. A society grows up by sequentially incorporating new members. The negotiations are always bilateral. We study this protocol in the context of non-transferable utility (NTU) games in characteristic function form. When the corresponding NTU game (N,V) satisfies that V(N) is flat, the only payoff which arises in equilibrium is the Shapley NTU value.Shapley NTU value, sequential formation of coalitions, subgame perfect equilibrium

A characterization of the nn-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem

A theorem of single-sorted algebra states that, for a closure space $(A,J)$ and a natural number $n$, the closure operator $J$ on the set $A$ is $n$-ary if, and only if, there exists a single-sorted signature $\Sigma$ and a $\Sigma$-algebra $\mathbf{A}$ such that every operation of $\mathbf{A}$ is of an arity $\leq n$ and $J = \mathrm{Sg}_{\mathbf{A}}$, where $\mathrm{Sg}_{\mathbf{A}}$ is the subalgebra generating operator on $A$ determined by $\mathbf{A}$. On the other hand, a theorem of Tarski asserts that if $J$ is an $n$-ary closure operator on a set $A$ with $n\geq 2$, and if $i<j$ with $i$, $j\in \mathrm{IrB}(A,J)$, where $\mathrm{IrB}(A,J)$ is the set of all natural numbers $n$ such that $(A,J)$ has an irredundant basis ($\equiv$ minimal generating set) of $n$ elements, such that $\{i+1,\ldots, j-1\}\cap \mathrm{IrB}(A,J) = \varnothing$, then $j-i\leq n-1$. In this article we state and prove the many-sorted counterparts of the above theorems. But, we remark, regarding the first one under an additional condition: the uniformity of the many-sorted closure operator

Eilenberg theorems for many-sorted formations

A theorem of Eilenberg establishes that there exists a bijection between the set of all varieties of regular languages and the set of all varieties of finite monoids. In this article after defining, for a fixed set of sorts $S$ and a fixed $S$-sorted signature $\Sigma$, the concepts of formation of congruences with respect to $\Sigma$ and of formation of $\Sigma$-algebras, we prove that the algebraic lattices of all $\Sigma$-congruence formations and of all $\Sigma$-algebra formations are isomorphic, which is an Eilenberg's type theorem. Moreover, under a suitable condition on the free $\Sigma$-algebras and after defining the concepts of formation of congruences of finite index with respect to $\Sigma$, of formation of finite $\Sigma$-algebras, and of formation of regular languages with respect to $\Sigma$, we prove that the algebraic lattices of all $\Sigma$-finite index congruence formations, of all $\Sigma$-finite algebra formations, and of all $\Sigma$-regular language formations are isomorphic, which is also an Eilenberg's type theorem.Comment: 46 page